Delhi Police Constable Exam Model Paper 8

A person covers $\frac{1}{3^{\mathit{r}\mathit{d}}}$ of a distance with the speed of = 10 km / hr
A person covers next $\frac{1}{3^{\mathit{r}\mathit{d}}}$ of a distance with the speed of = 20 km / hr
Rest distance covers with the speed of = 40 km / hr
Formula:
Average speed = Total distance / total time
Calculation:
Let total distance be 120 km
$\frac{1}{3^{\mathit{r}\mathit{d}}}$ of total distance $=120\times \left(\frac{1}{3}\right)=40$ km
$\frac{1}{3^{\mathit{r}\mathit{d}}}$ of total distance = $120\times \left(\frac{1}{3}\right)=40$ km
Remaining distance $=120-40-40=40$ km
Time taken by person to cover 40 km distance with the speed of 10 km / hr = 40 / 10 = 4 hrs
Time taken by person to cover 40 km distance with the speed of 20 km / hr = 40 / 20 = 2 hrs
Time taken by person to cover 40 km distance with the speed of 40 km / hr = 40 / 40 = 1 hr
Total time = $4+2+1=7$ hrs
∴ Average speed = 120/7 km/hr